2,784 research outputs found
Multiple positive solutions for functional dynamic equations on time scales
AbstractIn this paper, we study the following functional dynamic equation on time scales: {[Φ(uΔ(t))]∇+a(t)f(u(t),u(μ(t)))=0,t∈(0,T)T,u(t)=φ(t),t∈[−r,0)T,u(0)−B0(uΔ(0))=0,uΔ(T)=0, where Φ:R→R is an increasing homeomorphism and a positive homomorphism and Φ(0)=0. By using the well-known Leggett–Williams fixed point theorem, existence criteria for multiple positive solutions are established. An example is also given to illustrate the main results
(Benzoato-κO)bis(1,10-phenanthroline-κ2 N,N′)copper(II) chloride benzoic acid disolvate
In the title complex, [Cu(C7H5O2)(C12H8N2)2]Cl·2C6H5COOH, the CuII ion is coordinated by one carboxylate O atom from a benzoate anion and four N atoms from two phenantroline ligands in a distorted five-coordinate trigonal-bipyramidal CuON4 chromophore. The Cu2+ and the Cl− ion are imposed by a twofold rotation axiss which also bisects the equally disordered benzoate anion. In the crystal, the molecules are assembled into chains along [010] by C—H⋯Cl, O—H⋯Cl and C—H⋯O hydrogen-bonding interactions. The resulting chains are further connected into two-dimensional supramolecular layers parallel to [100] by interchain π⋯π stacking interactions [centroid–centroid distance = 3.823 (5) Å] between the phenanthroline ligands and the benzoic acid molecules, and by C—H⋯O hydrogen-bonding interactions. Strong π⋯π stacking interactions between adjacent phenantroline ligands [3.548 (4) Å] assemble the layers into a three-dimensional supramolecular architecture
Exposure of the Hidden Anti-Ferromagnetism in Paramagnetic CdSe:Mn Nanocrystals
We present theoretical and experimental investigations of the magnetism of
paramagnetic semiconductor CdSe:Mn nanocrystals and propose an efficient
approach to the exposure and analysis of the underlying anti-ferromagnetic
interactions between magnetic ions therein. A key advance made here is the
build-up of an analysis method with the exploitation of group theory technique
that allows us to distinguish the anti-ferromagnetic interactions between
aggregative Mn2+ ions from the overall pronounced paramagnetism of magnetic ion
doped semiconductor nanocrystals. By using the method, we clearly reveal and
identify the signatures of anti-ferromagnetism from the measured temperature
dependent magnetisms, and furthermore determine the average number of Mn2+ ions
and the fraction of aggregative ones in the measured CdSe:Mn nanocrystals.Comment: 26 pages, 5 figure
Study on the layered dusty plasma structures in the summer polar mesopause
Traditional hydrodynamic equations are adopted to build a
one-dimensional theoretical model to study the effect of gravity
wave on layered dusty plasma structures formation and evolution near
the polar summer mesospause region associated with polar mesosphere
summer echoes (PMSE). The proposed mechanism gives consideration to
the charged ice particle motion by the gravity wave modulation,
making a significant contribution to the vertical transport of heavy
ice particles and convergence into thin layers. And numerical
results show that the pattern of the multi-layer structure depends
on the ration of the initial ice particles density distribution to
the vertical wavelength of the gravity waves, the ice particle size
and the wind velocity caused by gravity wave. Also, the variation of
ion density distribution under the influence of gravity wave has
also been examined. Finally, the electron density depletions
(bite-outs) layers has been simulated according to the charge
conservation laws, and the results are compared to the ECT02 rocket
sounding data, which agree well with the measuring
Role of AC-cAMP-PKA Cascade in Antidepressant Action of Electroacupuncture Treatment in Rats
Adenylyl cyclase (AC)-cyclic adenosine monophosphate (cAMP)-cAMP-dependent protein kinase A (PKA) cascade is considered to be associated with the pathogenesis and treatment of depression. The present study was conducted to explore the role of the cAMP cascade in antidepressant action of electroacupuncture (EA) treatment for chronic mild stress (CMS)-induced depression model rats. The results showed that EA improved significantly behavior symptoms in depression and dysfunction of AC-cAMP-PKA signal transduction pathway induced by CMS, which was as effective as fluoxetine. Moreover, the antidepressant effects of EA rather than Fluoxetine were completely abolished by H89, a specific PKA inhibitor. Consequently, EA has a significant antidepressant treatment in CMS-induced depression model rats, and AC-cAMP-PKA signal transduction pathway is crucial for it
Silicon nitride metalenses for unpolarized high-NA visible imaging
As one of nanoscale planar structures, metasurface has shown excellent
superiorities on manipulating light intensity, phase and/or polarization with
specially designed nanoposts pattern. It allows to miniature a bulky optical
lens into the chip-size metalens with wavelength-order thickness, playing an
unprecedented role in visible imaging systems (e.g. ultrawide-angle lens and
telephoto). However, a CMOS-compatible metalens has yet to be achieved in the
visible region due to the limitation on material properties such as
transmission and compatibility. Here, we experimentally demonstrate a divergent
metalens based on silicon nitride platform with large numerical aperture
(NA~0.98) and high transmission (~0.8) for unpolarized visible light,
fabricated by a 695-nm-thick hexagonal silicon nitride array with a minimum
space of 42 nm between adjacent nanoposts. Nearly diffraction-limit virtual
focus spots are achieved within the visible region. Such metalens enables to
shrink objects into a micro-scale size field of view as small as a single-mode
fiber core. Furthermore, a macroscopic metalens with 1-cm-diameter is also
realized including over half billion nanoposts, showing a potential application
of wide viewing-angle functionality. Thanks to the high-transmission and
CMOS-compatibility of silicon nitride, our findings may open a new door for the
miniaturization of optical lenses in the fields of optical fibers,
microendoscopes, smart phones, aerial cameras, beam shaping, and other
integrated on-chip devices.Comment: 16 pages, 7 figure
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